Generalized Dedekind sums

Numerical semigroups, Dedekind sums and Alexander polynomials of torus knots

We connect Dedekind sums and Alexander polynomials of torus knots.

TQFT中签名的量子模性与广义 Dedekind 和

Quantum modularity of signatures in TQFT and generalized Dedekind sums

本文通过量子模性方法证明了 SU(2)-TQFT 在 genus 2 表面的签名与广义 Dedekind 和的关联，并展示了其与 Eichler 积分的关系。

Adiabatic limits of Seifert fibrations, Dedekind sums, and the diffeomorphism type of certain 7-manifolds

We extend the adiabatic limit formula for eta-invariants by Bismut-Cheeger and Dai to Seifert fibrations. Our formula contains a new contribution from the singular fibres that takes the form of a generalised Dedekind sum. As an application, we compute the Eells-Kuiper and t-invariants of certain cohomogeneity one manifolds that were studied by Dearricott, Grove, Verdiani, Wilking, and Ziller. In particular, we determine the diffeomorphism type of a new manifold of positive sectional curvature.

Heegaard Floer correction terms and Dedekind-Rademacher sums

We derive a closed formula for the Heegaard Floer correction terms of lens spaces in terms of the classical Dedekind sum and its generalization, the Dedekind-Rademacher sum. Our proof relies on a reciprocity formula for the correction terms established by Ozsvath and Szabo. A consequence of our result is that the Casson-Walker invariant of a lens space equals the average of its Heegaard-Floer correction terms. Additionally, we find an obstruction for the equality and equality with opposite sign, of two correction terms of the same lens space. Using this obstruction we are able to derive an opt…

额外扭曲连通和的Nu不变量

Nu-invariants of extra-twisted connected sums

本研究推广了G₂流形的扭曲连通和构造，将扩展nu不变量分解为不动点与粘合贡献，结合数论论证证明了存在非G₂零配边的紧G₂流形。